SOLUTION: Paige turner loves finite mathematics. She has 5 books about probability and four books about matrices. She lends her friend Anita Tudor four of these books, selected completely ra

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Question 1182308: Paige turner loves finite mathematics. She has 5 books about probability and four books about matrices. She lends her friend Anita Tudor four of these books, selected completely random.
What is the probability Paige lends Anita two books on each topic (I.e. two matrix books and two probability books)?
What is the probability she lends her at least one book on each topic?
Enter your answers as fractions in lowest terms.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
for 2 each it would be 5C2*4C2/9C4, the 9C4 is choosing 4 books from 9. It is also the "sum" of the two top terms.
=10*6/126 or 60/126=10/21
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for at least 1 on each topic. Look at the possibility of none for each topic. That is 4C0*5C4/9C4=5/126
and 5C0*4C!/9C4=4/126. We want everything but these two possibilities, which is 117/126=13/14.